Dynamc Rng n Self-Healng MPS Networs Krzysztof Walowa Char of Systems and Computer Networs, Faculty of Electroncs, Wroclaw Unersty of Technology, Wybrzeze Wyspansego 27, 50-370 Wroclaw, Poland walowa@zss.pwr.wroc.pl Abstract. Modern computer networs requre self-healng capabltes. Selfhealng s the ablty of a computer networ to reconfgure tself around falures such that calls n progress are not dropped and suffer no or almost no degradaton n qualty of serce. Proson of self-healng n MPS (MultProtocol abel Swtchng) networs n a cost effecte manner s an mportant problem. In ths wor we consder ssues of dynamc rng n self-healng MPS networs. We deelop new functons and ln metrcs for robust establshng of SPs (label swtched paths). We compare performance of new metrcs to other ln metrcs used n rng algorthms. As the performance ndcator we apply the lost flow functon. Smulatons show that proposed metrcs prode from 8% to 18% better results than the standard hop-number metrc. 1 Introducton IP networs propose scalablty and flexblty for rapd deployment of alue added IP serces. Neertheless, the ncreasng demand and explose growth of the Internet cause that carrers requre a networ nfrastructure that s dependable, predctable and offers relable networ performance. Effcent rng and traffc engneerng are the two foundatons needed to accomplsh surable networng. Moreoer, sgnfcant networng features such as path optmzaton, reslence and falure recoery are also mportant for bacbone networs to deler relable serces to customers usng the networ for msson-crtcal busness. The MultProtocol abel Swtchng (MPS) approach proposed by the Internet Engneerng Tas Force (IETF) s a networng technology that enables delerng traffc engneerng capablty and QoS performance for carrer networs. An MPS node that s capable of forwardng IP pacets and supports MPS s called a label swtchng rer (SR). The path through one or more SRs at one leel of the herarchy followed by a pacet n a partcular FEC (Forwardng Equalence Class) s nown as a label swtched path (SP). Accordng to [12] self-healng s the ablty of a computer networ to reconfgure tself around falures such that calls n progress are not dropped and suffer no or almost no degradaton n qualty of serce. Proson of self-healng abltes n MPS networs n a cost effecte manner s a sgnfcant ssue. The man dea of prodng self-healng capabltes n computer networs conssts n prodng spare capacty aalable on networ lns. If a networ ln fals, the pacets wll be dstrbuted among remanng lns usng spare capacty of these lns.
Most of self-healng methods use sharng of spare capacty for arous falure eents. Ths approach yelds a cost effecte self-healng restoraton. Prodng self-healng ncludes many aspects: spare capacty allocaton, rerng strateges, how traffc s dstrbuted, falure detecton, propagaton of nformaton ab falure, networ control [1], [8]. In ths wor we focus on problems of spare capacty allocaton n exstng MPS networs. We consder an exstng MPS networ,.e. the networ topology and ln capacty are gen. Our man goal s to prode res for all demands n order to use the networ capacty effcently n terms of networ relablty. It must be noted that hang the networ resource and a traffc demand, the res assgnment determnes spare capacty allocaton oer the networ. Thus, assgnment of res has an effect on the amount of flow restored when a falure occurs [9]. Therefore, the man objecte of ths paper s to deelop new metrcs (weghts) for res calculaton. Usng these metrcs should prode effecte allocaton of spare capacty that enables restoraton of flow after a networ falure. To mae an ealuaton of proposed metrcs we compare performance of these metrcs wth performance of other metrcs used n non-relable dynamc rng, e.g. the hopnumber metrc. Results of extense smulaton tests are presented and dscussed. 2 Self-healng MPS Networs Self-healng MPS networs realze fast restoraton from a networ falure by swtchng affected SPs oer alternate res. There are two models for path recoery n MPS: rerng and protecton swtchng. Recoery by rerng s defned as establshng new paths on demand for restorng traffc after the occurrence of a falure. The recoery paths may be found usng networ rng polces, precomputed confguratons and networ topology nformaton. After detectng a falure, paths are establshed usng sgnalng. Snce more operatons must be done, rerng s much slower than protecton swtchng mechansm. Howeer, whle networ resources hae not to be resered untl the falure, rerng s easer. Protecton swtchng recoery mechansms use preestablshed recoery paths, based upon networ rng polces, the restoraton requrements of the traffc on the worng path, and admnstrate consderatons. When a falure occurs, the protected traffc s swtched oer to the recoery path(s) and restored. It must be noted that protecton swtchng and rerng may be used together. For nstance, n order to recoer onlne a faled path and prode connectty protecton swtchng may be used. Rerng may be appled to determne a new optmal networ confguraton and rearrange paths n offlne manner [11]. There are three confguratons of worng and recoery paths for rerng and protecton swtchng n MPS networs [2], [3], [11]: ocal repar. Known also as local recoery, protects the worng path aganst a ln or neghbor node falure. ocal repar can be of two types: ln recoery/restoraton, node recoery/restoraton. The former one assumes, that the recoery path res around a faled ln. The alternate path s found between the two SRs on the ends of a faled ln. In latter case, the recoery path may be confgured to re around a faled neghbor node. The man adantage of local repar s
fast propagaton of a falure nformaton and smplcty. The node upstream of the falure s responsble for ntaton of the recoery process and swtchng the traffc to a recoery path. Global repar. The man dea of global repar, called also edge-to-edge rerng, s to protect the worng path aganst any ln or node fault on a path, except the falures occurrng at the ngress node of the protected path. It means that the recoery path must be ln and node dsjont from the worng path. It has the adantage of protectng aganst all ln and node falures on the worng path. The man drawbac s slower reacton to a falure than for local repar. Reerse bacup. In the reerse bacup approach the traffc of faled ln s reersed from the pont of a falure,.e. the ngress node of the faled ln, bac to the source (ngress) node of the protected worng path. That node reres ncomng traffc to alternate recoery paths. Major beneft s relately small tme of restoraton, snce the falure notfcaton s smplfed. The man dsadantage s reduced resource utlzaton. Two recoery paths are needed: one from the pont of falure to the ngress node of the path and the second one from the ngress node to the egress node of the protected path. SR4 SR4 SR4 SR7 SP worng path SR7 SP worng path SR7 SP worng path SP recoery path SR3 SP recoery path SR3 SP recoery path SR3 SR6 SR6 SR6 SR2 SR2 SR2 SR5 SR5 SR5 SR1 SR1 reerse bacup SP SR1 (a) (b) (c) Fg. 1. MPS rerng strateges: (a) Global repar, (b) ocal repar, (c) Reerse bacup Fg. 1 llustrates three confguratons of worng and recoery paths for rerng and protecton swtchng. The worng SP 1-2-3-4 connectng SR1 and SR 4 s broen when the ln 2-3 fals. For global repar the node 1 s nformed ab the falure and s responsble for rerng the traffc to a recoery path 1-5-6-7-4 (Fg.1a). In local repar scheme, the SR2 reres to a recoery path 2-7-3 to omt the faled ln (Fg. 1b). It results n a recoery path 1-2-7-3-4 for demand par SR1- SR4. For reerse bacup approach, SR2 reres to a reerse bacup SP 2-1. Then SR1 reres the traffc to a recoery path 1-5-6-7-4 (Fg. 1c).
For local repar, global repar and reerse bacup the recoery path may be preestablshed or dynamcally sought after notfcaton of a falure. The former approach prodes effecteness and small recoery tme. Resources of pre-establshed recoery paths may be resered n order to ncrease relablty. The latter approach s ery flexble. Howeer, snce some traffc may not be restored due to lmted networ resources, t doesn t guarantee hgh relablty [3]. 3 Functons for SPs Rerng MPS supports two methods of re selecton: hop-by-hop rng, and explct rng [10]. In ths wor we apply the explct rng. Explct rng assumes that a sngle SR, usually the SP ngress node, specfes seeral or all SRs n the SP. Therefore, t s a nd of source-destnaton rng. Accordng to [7] sourcedestnaton rng enables prodng traffc engneerng and polcy rng better then tradtonal hop-by-hop destnaton orented rng. ns that are congested can be aoded wth rng decsons made at the SP ngress node. Moreoer, the use of dynamc ln metrc nstead of statc ln metrc facltates selecton of good paths that meets the requred QoS parameters. We focus on two rerng methods: local repar and reerse bacup. Recall that n both schemes the node upstream of the falure s responsble for ntaton of the recoery process and swtchng the traffc to a recoery path. Therefore, that node s the potental bottlenec of the restoraton process. More precsely, the flow of the faled ln must be rered usng other lns leang the consdered node, excludng the faled ln. The resdual capacty of these lns s an upper bound of the flow that can be restored. We defne resdual (spare) capacty of a ln as a dfference between ln capacty and flow of that ln. The ln flow s a sum of all SPs flows usng that ln. Snce the resdual capacty s used for rerng of faled SPs, t s ery mportant to locate resources of resdual capacty effectely. The central dea of our approach s to deelop new objecte functons for worng res assgnment. Such functons should ndcate preparaton of the networ to the rerng. Next, these functons can be used to deelop ln metrcs for re calculaton. We consder an exstng MPS,.e. we do not consder capacty plannng and topologcal desgn. We mae an assumpton that for restoraton of faled SPs the dynamc rerng after the occurrence of a falure s appled. We model MPS networ as a drected graph G=(N,A,C) where N s a set of n nodes (ertces) representng networ swtches, A s a set of m arcs (drected edges) representng networ lns and C s a ector of ln capacty. We denote by o : A V and d : A V functons defnng the orgn and destnaton node of each arc. For each A n ( a) = A d( ) = d( a), a a we call { } the set of ncomng arcs of d(a) except a, and ( a) = { A ) = a), a} the set of gong arcs of a) except a. To mathematcally represent the problem, we ntroduce the followng notatons f Represents the total flow on arc a. a
c The capacty of arc a. a g = f : ) = Aggregate flow of gong arcs of. n g = f Aggregate flow of ncomng arcs of. : d( ) = e = c Aggregate capacty of gong arcs of. : ) = n e = c Aggregate capacty of ncomng arcs of. : d( ) = We model the MPS flow as non-bfurcated multcommodty (m.c) flow denoted by f = [ f 1, f 2,..., f m ]. f s a ector of flows n all arcs. We call a m.c. flow f ald f for eery arc a A the capacty constrant holds. For more nformaton on m.c. flows refer to [5]. For the sae of smplcty we ntroduce the followng functon 0 for x 0 (1) ε ( x) = x for x > 0 To analyze the local repar and reerse bacup strateges we consder an arc A. We assume falure of. Recall that consdered rerng methods assume that flow on the arc must be rered by the source node of the arc. Therefore, spare capacty of gong arcs of ) except s a potental bottlenec of the rerng. Notce that f f ( c f ) (2) ( ) then flow of the faled arc can be restored usng spare capacty of other arcs leang the orgn node of. Recallng defnton of g ) and e ) we can reformulate (2) n the followng way g o e ( ) ) c (3) Otherwse, f f > ( c f ) (4) ( ) then some flow of the faled ln cannot be restored, snce spare capacty of other arcs leang the orgn node of s too small. It means that these arcs bloc the 100% restoraton and some flow of arc s lost. Recallng defnton of g ) and e ) we can reformulate (4) n the followng way g o > e ( ) ) c (5)
We defne the flow of lost n the node ) as flow that cannot be restored usng other arcs leang ) due to lmted resources of spare capacty as follows ( g ( e c )) ( f ) =ε (6) ) ) The functon depends on the flow g ) leang the node ). s not dependent drectly on the flow f of the arc. It means that changng the flow on other arcs leang the node ) modfes alue of the functon. Therefore, we formulate a functon N of lost flow leang the node as a sum of functons oer all arcs leang that node N Note that functons ( g ( e c )) ( f ) = ( f ) = ε (7) : ) = : ) = and N prode a good metrc for reerse bacup rerng. In the same way as functons and n N N n n n and N ( g ( e c )) n d ( ) n d ( ), we can defne functons ( f ) =ε (8) n n ( g ( e c )) n ( f ) = ( f ) = ε (9) : d ( ) = : d( ) = The functon denotes lost flow that cannot be restored usng arcs enterng the n node d() due to lmted spare capacty of these arcs. Correspondngly, N s a lost flow enterng the node. n ( f ), ( f ), N ( f ) and N ( f ) are contnuous, non-decreasng, pece-wse lnear and conex functons for any ald flow f. The formal proof of these propertes can be found n [13]. Moreoer, functon ( f ) s a lower bound of the lost flow for reerse bacup rerng of arc. It must be noted that authors of [8] hae ntroduced smlar approach for local rerng of ATM networ. They formulated a problem of worng res assgnment wth the objecte functon of lost flow usng the -shortest path based rerng. For local repar all SPs usng must be rered around after falure of ths arc. In order to estmate the amount of the restored flow, the maxmum flow algorthm can be appled. The maxmum flow crteron denotes the theoretcal maxmal rerng capacty. In ths method, the faled arc s remoed from the networ. Next, maxmum flow between the orgn and destnaton node of s calculated. Another performance ndcator for local repar s -shortest paths (KSP) algorthm, whch fnds - successely shortest dsjont paths n a graph. Authors of [4] compared these two n n
strateges usng smulaton methods. KSP restoraton offers performance 99.9% of that from Max Flow. The adantage of KSP s tme complexty of O(nlogn) compared to maxmum flow O(n 3 ) usng the centralzed restoraton by a sngle processor computaton. et () denote flow of the faled arc restored by the maxmum flow method. We formulate a functon of lost flow due to a falure of arc usng maxmum flow restoraton method as follows ( f ( )) ( f ) =ε (10) Functon ( f ) prodes a theoretcal mnmal alue of flow lost after the local repar of. It can be nterpreted as a performance ndcator used here to measure the networ performance n terms of self-healng capabltes. 4 Defntons of n Metrcs Man goal of ths wor s to deelop and ealuate new ln metrcs for computaton of SPs. Res should be set up n such a way that the networ wll be prepared to rerng of faled SPs. Snce the resdual capacty wll be located effcently, the networ wll be better arranged to the rerng of all faled SPs. As mentoned aboe, we apply the explct rng of MPS that enables the ngress SR of SP to specfy all SRs n the SP. We use a partal nformaton model proposed n [6]. In ths model the nformaton aalable to the rng algorthm s the total bandwdth usage for each ln. It means that each SR n the networ has the nowledge on the networ topology, capacty and flow n each ln. Author of [7] proposed to apply an extended erson of ln state rng protocol to obtan these nformaton. We concentrate on addte metrcs,.e. the path s length s equal to the sum of the correspondng metrcs of the lns along that path. Another possblty, not consdered n ths wor, s to use nonaddte metrcs. In ths case the alue of a path s the mnmum (or maxmum) ln metrc along that path. We mae an assumpton that all SPs are not nown a pror. Therefore, the dynamc onlne rng of SPs s requred. Each new SP s re s determned usng the shortest path algorthm applyng selected ln metrcs usng the nformaton on ln capacty and ln aggregate flow. Applyng functons defned n the preous secton, we deelop three new metrcs that can be used for computaton of SPs shortest res. In order to mae easer the consderaton we ntroduce a new functon 0 ϖ ( x) = 1 Next we defne the followng functon for for x 0 x > 0 (11)
( g ( e c )) τ ( f ) = ϖ (12) : ) = Note that τ ( f ) (12) s a derate of N ( f ) (7) for a ald flow f except ponts g = e c ) for all : ) =. In these ponts the functon τ ( f ) s ( equal to the left-sded derate of the functon N ( f ). Smlar we can defne the n functon τ ( f ) n n ( g ( e c )) n τ ( f ) = ϖ (13) : d ( ) = The new metrcs for the shortest re path calculaton are defned as follows N l 1+ τ ) = (14) l = 1+ 0.5( τ + τ ) (15) n ) d ( ) l max = 1+ max( τ, τ ) (16) ) n d ( ) Metrcs (14-16) are formulated n order to locate resources of spare capacty n the best way n terms of the networ relablty. To mae a comprehense ealuaton of these three new metrcs, we compare ther performance wth other four metrcs l 1 = 1 (17) f l = f (18) f /( c l 1/( c l f ) f (19) = ( c f ) f ) 1 (20) = ( c f ) Metrcs (17-20) drectly don t tae nto account any relablty crtera. The metrc (17), called the hop-number metrc, s wdely used n many rng protocols.
5 Results We made extense tests oer 10 arous networs wth the number of nodes aryng from 10 to 18 (see Table 1). Table 1. Parameters of tested networs Name Number of nodes Number of lns Aerage node degree (and) Number of paths Number of tests 1034 10 34 3.40 90 4 1038 10 38 3.80 90 4 1042 10 42 4.20 90 5 1046 10 46 4.60 90 5 1450 14 50 3.57 182 12 1456 14 56 4.00 182 10 1462 14 62 4.43 182 10 1866 18 66 3.66 306 9 1874 18 74 4.11 306 9 1882 18 82 4.56 306 9 The methodology of tests s as follows. All SPs, one by one, are processed. Each SP s represented by the orgn node, destnaton node and bandwdth requrement. A shortest path algorthm accordng to the consdered metrc fnds the worng re. If t s mpossble to establsh a new SP due to capacty constrants, the SP s rejected. When all SPs hae been processed, the followng functons representng the performance ndcators are calculated ( f ) = F ( f ) A (21) N ( f ) = N ( f ) A (22) Recall that the functon defnes the theoretcal mnmal alue of flow lost n a networ usng the local repar due to a sngle falure of any arc. The functon N s an estmaton the flow lost n the networ due to a sngle falure of any ln for reerse bacup rerng strategy. Both functons can be consdered as the performance ndcators used here to measure networ performance. These two functons ndcate the preparaton of the networ to the restoraton process. If alue of functons and N s low, more flow s restored after a falure. As a thrd performance ndcator we used the number of rejected calls (NRC),.e. the number of SPs, whch are not set up due to lmted resources of the capacty. The same set of SPs s processed for all metrcs (14-20) defned n preous secton. We can see n Table 2 that results for metrcs (18-20) are much worse than for other four metrcs. Values of functon for metrcs (14-16) are lower than for the hop-number metrc (17) respectely by 8%, 12% and 10%. For N functon
metrcs (14-16) hae een better performance comparng to the hop-number metrc and the dfference s respectely 14%, 18%, and 14%. Howeer, the hop-number metrc prodes the lowest number of rejected SPs gen by the NRC functon. Table 2. Results of all tests Metrcs Functon 1 f f/(c-f) 1/(c-f) N max 221394 314687 337261 377719 204078 195365 200236 N 110104 198341 231895 252241 94159 90702 94689 NRC 322 499 647 725 360 355 361 To present the results on Fg. 2 and Fg. 3, the amount of lost flow calculated accordng to the functon (21) s normalzed wth the respect to the ln capacty. NF s defned as a unt of normalzed lost flow where 100 NF s equal to the capacty of all lns n the networ. Fg. 2 presents alues of the normalzed lost flow functon for all tested networs. Performance of metrcs (14-17) s shown. We can see that for arous networs (n terms of the and parameter denotng the aerage node degree) new metrcs prode better performance than the hop-number metrc. Normalzed ost Flow NF 50 45 40 35 30 25 20 15 10 5 0 3,30 3,50 3,70 3,90 4,10 4,30 4,50 4,70 and Fg. 2. Graph showng performance of metrcs N,, max, hop-number as a functon of the aerage node degree On the Fg. 3 we can see performance of metrcs (14-17) for the networ 1882 as a functon of the networ aerage ln utlzaton (alu). The alu parameter s a quotent of the oerall networ flow and capacty of all lns. The performance s denoted by normalzed lost flow. When the load s not heay, metrcs (14-16) prode much better performance than the metrc (17). For more saturated networs results of all metrcs are much more smlar. N max 1
6 Concludng Remars The two man contrbutons n ths paper are the deelopment of new metrcs for dynamc SPs calculaton and a comparate analyss of these metrcs and other metrcs wth respect to MPS constrants. Accordng to obtaned results the networ usng new metrcs s better prepared to the restoraton process. Therefore, applyng new metrcs leads to mproed performance of the networ n terms of self-healng capabltes. The expermental data s reasonably well explaned by the hypothess that new metrcs tae nto consderaton ssues of networ relablty and spare capacty allocaton. Other tested metrcs don t consder drectly spare capacty allocaton. Another concluson s that performance of metrcs (14-16) s better for less congested networs. As aerage ln utlzaton ncreases, the hop-number metrc ges results comparable to results of metrcs (14-16). Furthermore, the comparson of metrcs shows that the performance doesn t depend on the aerage node degree parameter. An addtonal adantage of ths paper s that proposed approach can be appled to both centralzed and dstrbuted control scenaros of self-healng networs. Normalzed ost Flow NF 40 35 30 25 20 15 10 5 N max 1 0 0,42 0,47 0,52 0,57 0,62 0,67 0,72 alu Fg. 3. Graph showng performance of metrcs N,, max, hop-number as a functon of the aerage ln utlzaton for the networ 1882 For desgn of computer networs we can use offlne or onlne algorthms. Aboe we dscussed the possblty of applyng new objecte functons and new metrcs for dynamc, onlne rng. For offlne algorthms functons deeloped n secton 3 can be appled as objecte functons n the optmzaton problem of statc res assgnment. For more nformaton refer to [13], [14]. In future wor we plan to compare our approach to the path cachng framewor proposed n [7]. Furthermore, we want to extend our research on nonaddte metrcs (e.g. aalable bandwdth, resdual capacty) and compare performance of deeloped aboe addte metrcs wth nonaddte metrcs.
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